When migrating between different O365 subscriptions at the site level this error is generated. It is not generated if migrating at the list or item level:
The server sent HTTP status code 403: Forbidden: The server sent HTTP status code 403: Forbidden
Please ensure the user account you have supplied for both source and target sites has full site administrator permission. If the permissions are correct then this error occurs because you are migrating to and from O365 and the Maximum Parallel Threads variable is set to a number higher than 1.
When migrating between different O365 subscriptions at the site level if multiple threads are established the error is generated because a connection has been established to both the source and target O365 sites at the same time. Due to the caching of authentication cookies that occurs with Internet Explorer if migrating between O365 subscriptions you can only use 1 thread which will mean the tool will connect to the source first, then the target rather than at the same time. The migration process will be slower but you will not have any errors.
To change this variable please do the following:
